Patterns of chiral symmetry breaking and a candidate for a C theorem in four dimensions

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We test a candidate for a four-dimensional C function. This is done by considering all asymptotically free, vectorlike gauge theories with Nf flavors and fermions in arbitrary representations of any simple Lie group. Assuming spontaneous breaking of chiral symmetry in the infrared limit and that the value of the C function in this limit is determined by the number of Goldstone bosons, we find that only in the case of a theory with two colors and fermions in one single pseudoreal representation of SU(2) does the C theorem seem to be violated. Conversely, this might also be a sign of new constraints, restricting the number of flavors consistent with spontaneous chiral symmetry breaking. For all other groups and representations we find that this candidate C function decreases along the renormalization-group flow.
Original languageEnglish
Pages (from-to)850421-850425
Number of pages5
JournalPhysical Review D
Issue number8 B
Publication statusPublished - 15 Apr 2002

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